ordered integral domain in English

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  "forms": [
    {
      "form": "ordered integral domains",
      "tags": [
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      "expansion": "ordered integral domain (plural ordered integral domains)",
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      "glosses": [
        "An integral domain which has a subset whose elements are said to be \"positive\", such that this subset is closed under addition, closed under multiplication, and all elements of the integral domain satisfy a law of trichotomy; namely, that either that element is in the said subset, or it is the zero (additive identity), or its product with −1 (the additive inverse of the multiplicative identity) belongs to the said subset."
      ],
      "hyponyms": [
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          "word": "ordered field"
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      "id": "en-ordered_integral_domain-en-noun-sLv1Sbsv",
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          "integral domain",
          "integral domain"
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          "trichotomy",
          "trichotomy"
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      "raw_glosses": [
        "(algebra) An integral domain which has a subset whose elements are said to be \"positive\", such that this subset is closed under addition, closed under multiplication, and all elements of the integral domain satisfy a law of trichotomy; namely, that either that element is in the said subset, or it is the zero (additive identity), or its product with −1 (the additive inverse of the multiplicative identity) belongs to the said subset."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "ordered integral domain"
}

[Show JSON for raw wiktextract data ▼] [Hide JSON for raw wiktextract data ▲]

{
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    {
      "form": "ordered integral domains",
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        "plural"
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      "expansion": "ordered integral domain (plural ordered integral domains)",
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      "word": "ordered field"
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      "glosses": [
        "An integral domain which has a subset whose elements are said to be \"positive\", such that this subset is closed under addition, closed under multiplication, and all elements of the integral domain satisfy a law of trichotomy; namely, that either that element is in the said subset, or it is the zero (additive identity), or its product with −1 (the additive inverse of the multiplicative identity) belongs to the said subset."
      ],
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        [
          "algebra",
          "algebra"
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        [
          "integral domain",
          "integral domain"
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          "trichotomy",
          "trichotomy"
        ]
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      "raw_glosses": [
        "(algebra) An integral domain which has a subset whose elements are said to be \"positive\", such that this subset is closed under addition, closed under multiplication, and all elements of the integral domain satisfy a law of trichotomy; namely, that either that element is in the said subset, or it is the zero (additive identity), or its product with −1 (the additive inverse of the multiplicative identity) belongs to the said subset."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "ordered integral domain"
}

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2025-01-15 from the enwiktionary dump dated 2025-01-01 using wiktextract (b941637 and 4230888). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

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"ordered integral domain" meaning in English

Noun

Inflected forms